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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 60v, page id 00068200:0122
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et habebitur: aa
2a4
aa
zax + axa
aa + 2cx + = XX
2aX + a XX
(s. jam X sit quadratus)
aa F2CX F C Xx habebitur
quaesitum, priau habebuntur
Naqu. 4aaq - 4a vvq+v
+ Vva
posterius habebitur sposito
quod  e affinmation)
sed sic melius:
sit xaqu yycode et
sive ZZ eq aa
perii
et 2a 4 a X et denque
si fairamus:
faciludo:
+c. fat
bb rax + a xr a siat aequ. Xx
 aequ
eote +a
Haec aequatio mutanta est in aliam rationalem,
sic ut assumta nova indeterminata v, secundum eam
vel Z dx=
quantitus  X aZu fat rationalis; ita enim figura
reducta erit, ad aliam homometram rationalem,
Itaque ponamus: E aeque
X lugu.
F ago. X + X, fiet:
va X qx
a (+
E KC aequ.
paxtax
seu vo troxie aequ e mo dan. 29b0
97
ratax
at
aqu h+Z. s sit (2+ +8 qu V. fiet:
  ago Z+ s _ -c aequ Z - 2 sC Ergo
a. per rationales
Ex his manifestum est, haberi s2zdx item
2a 7 a x aequ yy co eC
aequ
quia: bb a
2Z- ca
2AX + a XX
aa
habebitur:sad
seu quadratura figurae, ex dato XX (per rationales)
et aa + 2CX + = xxoq Vcorvee ex data (XX du qseu moment momento figurae
(41
Ergo 2a + a yy cowe aequyy1 ee
el.  aa + 2C yyco coe+
+Cyco ee aequ’yyco ée
et pro a  in aequ. 6.
ponendo valorem ex aequ. 4
fiet.
lac yycovex += ayyco eg
4 +
+ 2Cyycoco +Cyco e
aequ. yy loex. sive fiet
eaequ. habebitur e. sed
quoniam ista prolixiora,
satius redire statim ad X
ex tangente verticis  Habetur autem (Xxxdque si
modo habeatur: S. XY dx.: Ergo habebitur quadratura
figurae, si modo habeatur: (X3dx.. sed
XZ  aequ X quaabb 
2a X + 4aC XX f 2a cX
dx + fXX + gX + hiX
loco X scubatur ey. et fier:
dey + fecyyt gey Mhey
quantitas  quanda quadrato
ab lx + Cy + hCyy. quod
sub finem hujus plagulae fiet:
2a + ax, Z H nf a77
ergo tantum opus ut inveniatur aabb dq
24Z + a XZ
Habetur autem (xZ dqu, exdatasZ ax
aa FZCX + E XX raxtA XX
debet esse quadratus fiat multi
plicatio actu ipso:
+a XX +2a CX +
compendio
n7 Ax p
a ia 4
2Z43
aequ caa aa 2a dx 4 aa a x dx
rax F L XE (IIA F2) Lba
2Z ca
datur ergo 7+t 27- da xY sed haer
pendet ex tribus: (7)X dqueZX. et (Xdx
datur autem suexx per aqnationem primitivam
datur et
sa dx semper ergo datur
Ergo X_gus dque aequ aa d77 x 4 a xZ ax
 seu DaZ
Ergo 232 (2) bba dq aqu. 2aZ ax +  x Z x
- bbL
27 ca
aa X + L. dx
d + dxy et AZZAX p
est autem 1Z Z aequ. _ Mx iZ + a Ya. et Xxt  bb a
ergo fier: 6G aeq.
C +a
x + dy Y -bb c3
Z2. la
A
E Ca
_ faxx
+2, 14 49
sed inte habelus cantus  a dx + xta qudalinide possi
quq  29743
C aequ